Research Group in Global Analysis and Applications

http://globanal.upol.cz

Prof. RNDr. Demeter Krupka, DrSc. photo

Position:Adjunct Professor of Mathematics
Address:Department of Mathematics and Statistics
Faculty of Science, Technology and Engineering
School of Engineering and Mathematical Sciences
La Trobe University, Bundoora, 3086 Victoria, Australia
E-mail:name@latrobe.edu.au
Homepage:http://globanal.upol.cz/krupka.html
Honorary Position:IAS Distinguished Fellow, La Trobe University, Melbourne, www.latrobe.edu.au/ias/

List of Publications


Books and book chapters

  1. D. Krupka, Some Geometric Aspects of Variational Problems in Fibered Manifolds, Folia Fac. Sci. Nat. Univ. Purk. Brunensis, Physica 14, Brno, Czechoslovakia (1973) 65 pp.; arXiv:math-ph/0110005.
  2. D. Krupka and J. Musilová, Calculus of Odd Base Forms on Differential Manifolds, Folia Fac. Sci. Nat. UJEP Brunensis 24 (1983) 65 pp.
  3. D. Krupka, Natural Lagrangian structures, In: Differential Geometry (Banach Center Publications 12, Diff. Geom. Semester, Warsaw, Sept.-Dec. 1979, Polish Scientific Publishers, Warsaw, 1984) 185-210.
  4. D. Krupka and J. Janyška, Lectures on Differential Invariants (J. E. Purkyně University, Faculty of Science, Brno, Czechoslovakia, 1990) 193 pp.
  5. D. Krupka, Lectures on Variational Sequences, Advanced Texts in Mathematics, Open Ed. & Sci., Opava, Czech Republic, 1995, 94 pp.
  6. D. Krupka and M. Krupka, Jets and Contact Elements, In: Proceedings of the Seminar on Differential Geometry ((D. Krupka, Ed.) Mathematical Publications, Silesian University in Opava, Opava, Czechia, 2000) 39-85.
  7. D. Krupka, The Vainberg-Tonti Lagrangian and the Euler-Lagrange mapping, In: Differential Geometric Methods in Mechanics and Field Theory (Volume in Honour of W. Sarlet, (F. Cantrijn and B. Langerock, Eds.) Gent, Academia Press, 2007) 81-90.
  8. D. Krupka, Global variational theory in fibred spaces, In: Handbook of Global Analysis (Elsevier, 2008) 773-836.
  9. D. Krupka and D. Saunders (Eds.), Handbook of Global Analysis (Elsevier, 2008) 1229 pp.

Research articles

  1. D. Krupka, Lagrange theory in fibered manifolds, Rep. Math. Phys. 2 (1971) 121-133.
  2. D. Krupka, On the structure of the Euler mapping, Arch. Math. (Brno) 10 (1974) 55-61.
  3. D. Krupka, On generalized invariant transformations, Rep. Math. Phys. (Torun) 5 (1974) 353-358.
  4. D. Krupka and A. Trautman, General invariance of Lagrangian structures, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 22 (1974) 207-211.
  5. D. Krupka, A setting for generally invariant Lagrangian structures in tensor bundles, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 22 (1974) 967-972.
  6. D. Krupka, Lagrangians and topology, Scripta Fac. Sci. Nat. UJEP Brunensis, Physica 3-4 (1975) 265-270.
  7. D. Krupka, A geometric theory of ordinary first order variational problems in fibered manifolds, I. Critical sections, J. Math. Anal. Appl. 49 (1975) 180-206.
  8. D. Krupka, A geometric theory of ordinary first order variational problems in fibered manifolds, II. Invariance, J. Math. Anal. Appl. 49 (1975) 469-476.
  9. D. Krupka, A theory of generally invariant Lagrangians for the metric fields II, Internat. J. Theoret. Phys. 15 (1976) 949-959.
  10. D. Krupka, On a class of variational problems defined by polynomial lagrangians, Arch. Math. (Brno) 12 (1976) 99-106.
  11. D. Krupka, A map associated to the Lepagean forms of the calculus of variations in fibered manifolds, Czech. Math. J. 27 (1977) 114-118.
  12. D. Krupka, A theory of generally invariant Lagrangians for the metric fields I, Internat. J. Theoret. Phys. 17 (1978) 359-368
  13. D. Krupka, Elementary theory of differential invariants, Arch. Math. (Brno) 14 (1978) 207-214.
  14. D. Krupka and M. Horák, On the first order invariant Einstein-Cartan variational structures, Internat. J. Theoret. Phys.} 17 (1978) 573-584.
  15. D. Krupka, Mathematical theory of invariant interaction lagrangians, Czech. J. Phys. B 29 (1979) 300-303.
  16. D. Krupka, Fundamental vector fields on the type fibres of jet prolongations of tensor bundles, Math. Slovaca 29 (1979) 159-167.
  17. D. Krupka, Reducibility theorems for differentiable liftings in fibre bundles, Arch. Math. (Brno) 15 (1979) 93-106.
  18. D. Krupka, On the Lie algebras of higher differential groups, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 27 (1979) 235-239.
  19. D. Krupka, A remark on algebraic identities for the covariant derivatives of the curvature tensor, Arch. Math. (Brno) 16 (1980) 205-211.
  20. D. Krupka, Finite order liftings in principal fiber bundles, Beiträge zur Algebra und Geometrie 11 (1981) 21-27.
  21. D. Krupka, On the local structure of the Euler-Lagrange mapping of the calculus of variations, In: Proc. Conf. on Diff. Geom. Appl. (Nové Město na Moravě, Czechoslovakia, Sept. 1980, Charles University, Prague, 1982) 181-188.
  22. D. Krupka and M. Francaviglia, The Hamiltonian formalism in higher order variational problems, Ann. Inst. H. Poincaré, Sec. A 37 (1982) 295-315.
  23. D. Krupka, Local invariants of a linear connection, In: Differential Geometry (Colloq. Math. Soc. János Bolyai 31, North Holland, 1982) 349-369.
  24. D. Krupka, Lepagean forms in higher order variational theory, In: Modern Developments in Analytical Mechanics (Proc. IUTAM-ISIMM Sympos., Turin, June 1982, Academy of Sciences of Turin, 1983) 197-238.
  25. D. Krupka and J. Musilová, Integrals of motion in higher order mechanics and field theory (in Czech), Pokroky mat. fyz. astronom. 28 (1983) 259-266.
  26. D. Krupka and O. Štěpánková, On the Hamilton form in second order calculus of variations, In: Proc. Internat. Meeting "Geometry and Physics" (Florence, October 1982, Pitagora, Bologna, 1983) 85-101.
  27. D. Krupka and J. Musilová, Hamilton extremals in higher order mechanics, Arch. Math. (Brno) 20 (1984) 21-30.
  28. D. Krupka, On the higher order Hamilton theory in fibered spaces, In: Proc. Conf. on Diff. Geom. Appl. (Vol. 2, Nové Město na Moravě, Czechoslovakia, (D. Krupka, Ed.) Sept. 1983, J. E. Purkyně Univ., Brno, 1984) 167-184.
  29. D. Krupka and V. Mikolášová, On the uniqueness of some differential invariants, Czech. Math. J. 34 (1984) 588-597.
  30. D. Krupka and A. Sattarov, The inverse problem of the calculus of variations for Finsler structures, Math. Slovaca 35 (1985) 217-222.
  31. D. Krupka, Geometry of Lagrangean structures, 1. Odd base forms, Arch. Math. (Brno) 22 (1986) 159-174.
  32. D. Krupka, Geometry of Lagrangean structures, 2. Differential forms on jet prolongations of fibered manifolds, Arch. Math. (Brno) 22 (1986) 211-228.
  33. D. Krupka, Geometry of Lagrangean structures, 3. Lepagean forms and the first variation, In: Proc. 14th Winter School on Abstract Analysis (Srní, Czechoslovakia, Jan. 1986 Suppl. Rend. del. Circolo Mat. di Palermo, Ser. II, 1987) 187-224.
  34. D. Krupka, Regular Lagrangians and Lepagean forms, In: Differential Geometry and its Applications (Proc. Conf., Brno, Czechoslovakia, (D. Krupka and A. Švec, Eds.) August 1986, Kluwer Academic Publishers, 1987) 111-148.
  35. D. Krupka, Variational sequences on finite order jet spaces, In: Differential Geometry and its Applications (Proc. Conf., Brno, Czechoslovakia, (J. Janyška and D. Krupka, Eds.) August 1989, World Scientific, Singapore, 1990) 236-254.
  36. D. Krupka, Topics in the calculus of variations: Finite order variational sequences, In: Differential Geometry and its Applications (Proc. 5th Internat. Conf., Opava, Czechoslovakia, (O. Kowalski and D. Krupka, Eds.) Aug. 1992, Silesian University in Opava, 1993) 473-495.
  37. D. Krupka, The contact ideal, Diff. Geom. Appl. 5 (1995) 257-276.
  38. D. Krupka, The trace decomposition problem, Beiträge zur Algebra und Geometrie 36 (1995) 303-315.
  39. D. Krupka, The trace decomposition of tensors of type (1,2) and (1,3), In: New Developments in Differential Geometry (Proc. Colloq. on Diff. Geom., July 1994, Debrecen, (J. Szenthe and L. Tamássy, Eds.) Kluwer Academic Publishers, Dordrecht, 1996) 243-253.
  40. D. Krupka, Variational sequences in mechanics, Calc. Var. 5 (1997) 557-583.
  41. D. Krupka and D.R. Grigore, Invariants of velocities and higher order Grassman bundles, J. Geom. Phys. 24 (1998) 244-264.
  42. D. Krupka and J. Musilová, Trivial lagrangians in field theory, Diff. Geom. Appl. 9 (1998) 293-305.
  43. D. Krupka, J. Musilová and O. Krupková, The variational sequence in physical theories (in Czech), Čs. čas. pro fyziku A48 (1998) 330-341.
  44. D. Krupka and Dao Qui Chau, 3rd order differential invariants of coframes, Math. Slovaca 49 (1999) 563-576.
  45. D. Krupka, Variational sequences and variational bicomplexes, In: Differential Geometry and Applications (Proc. Conf., (I. Kolář, O. Kowalski, D. Krupka and J. Slovák, Eds.) Brno, August 1998, Masaryk University, Brno, Czech Republic, 1999) 525-531.
  46. D. Krupka and J. Musilová, Erratum: Trivial lagrangians in field theory, Diff. Geom. Appl. 9 (1998) 293-305; Diff. Geom. Appl. 10 (1999) 303.
  47. D. Krupka and J. Musilová, The variational sequence and trivial lagrangians (in Czech), In: Proc. 13th Conf. of Czech and Slovak Physicists (Zvolen, Slovakia, August 23 - 26, 1999, (M. Reiffers and L. Just, Eds.) The Zvolen Technical University, 2000) 328-331.
  48. D. Krupka and J. Musilová, Recent results in variational sequence theory, In: Steps in Differential Geometry (Proc. Colloq., (L. Kozma, P. T. Nagy and L. Támassy, Eds.) July 2000, Debrecen, Hungary, University of Debrecen, 2001) 161-186.
  49. D. Krupka, Global variational functionals on fibered spaces, Nonlinear Analysis 47 (2001) 2633-2642.
  50. D. Krupka, Natural projectors in tensor spaces, Beiträge zur Algebra und Geometrie 43 (2002) 217-231.
  51. D. Krupka, Variational principles for energy-momentum tensors, Rep. Math. Phys. 49 (2002) 259-268.
  52. D. Krupka, The Weyl tensors, Publ. Math. Debrecen 62 (2003) 447-460.
  53. D. Krupka and P. Musilová, Differential invariants of immersions of manifolds with metric fields, Rep. Math. Phys. 51 (2003) 307-313.
  54. D. Krupka, Global variational principles: Foundations and current problems, In: Global Analysis and Applied Mathematics (AIP Conference Proceedings 729, American Institute of Physics, 2004) 3-18.
  55. D. Krupka and J. Brajerčík, Variational principles for locally variational forms, J. Math. Phys. 46, 052903 (2005) 1-15.
  56. D. Krupka and J. Brajerčík, Variational principles on frame bundles, In: Differential Geometry and Its Applications (Proc. Conf., (J. Bureš, O. Kowalski, D. Krupka and J. Slovák, Eds.) Prague, August 2004, Charles University in Prague, Czech Republic, 2005) 559-569.
  57. D. Krupka and J. Šeděnková, Variational sequences and Lepage forms, In: Differential Geometry and Its Applications (Proc. Conf., (J. Bureš, O. Kowalski, D. Krupka and J. Slovák, Eds.) Prague, August 2004, Charles University in Prague, Czech Republic, 2005) 617-627.
  58. D. Krupka, O. Krupková, G. Prince and W. Sarlet, Contact symmetries and variational sequences, In: Differential Geometry and Its Applications (Proc. Conf., (J. Bureš, O. Kowalski, D. Krupka and J. Slovák) Prague, August 2004, Charles University in Prague, Czech Republic, 2005) 605-615.
  59. D. Krupka and J. Brajerčík, Noether currents and order reduction on frame bundles, In: Proc. 40th Sympos. on Finsler Geometry "In the Memory of our Teachers" (Hokkaido Tokai University, Sapporo, Society of Finsler Geometry, 2006) 34-37.
  60. D. Krupka, Trace decompositions of tensor spaces, Linear and Multilinear Algebra 54 (2006) 235-263.
  61. D. Krupka, The total divergence equation, Lobachevskii Journal of Mathematics 23 (2006) 71-93.
  62. D. Krupka, O. Krupková, G. Prince and W. Sarlet, Contact symmetries of the Helmholtz form, Differential Geometry and Applications 25 (2007) 518-542.
  63. D. Krupka and J. Brajerčík, Cohomology and local variational principles, Proc. of the XV International Workshop on Geometry and Physics (Puerto de la Cruz, Tenerife, Canary Islands, Spain, September 11–16, 2006, Publ. de la RSME, 2007) 119-124.
  64. D. Krupka, Natural variational principles, In: Symmetry and Perturbation Theory (SPT 2007, (G. Gaeta, R. Vitolo and S. Walcher, Eds.) Proc. Conf., Otranto, Italy, June 2-9, 2007, World Scientific, 2007) 116-123.
  65. D. Krupka, The structure of the Euler-Lagrange mapping, paper in honour of N.I. Lobachevskii, Russian Mathematics (Iz. VUZ) 51 (12) (2007), N.I. Lobachevskii Anniversary Volume, 52-70.
  66. A. Paták and D. Krupka, Geometric structure of the Hilbert-Yang-Mills functional, Int. J. Geom. Met. Mod. Phys. 5 (2008) 387-405.
  67. D. Krupka and O. Krupková, Contact symmetries and variational PDE's, Acta Appl. Math. 101 (1-3) (2008), A special issue dedicated to the 60th anniversary of Valentin Lychagin, 163-176.
  68. D. Krupka and Z. Urban, Differential invariants and higher order Grassmann bundles, In: Differential Geometry and its Applications (Proc. 10th Int. Conf. on Diff. Geom. and Appl., Olomouc 2007, World Scientific, Singapore, 2008) 463-473.

Dissertations

  1. D. Krupka, A contribution to the theory of weak interactions of strongly interacting particles (in Slovak), MSc thesis, J. E. Purkyně University, Brno, 1965.
  2. D. Krupka, Geometric Aspects of the Theory of Invariant Lagrange Structures, PhD (CSc.) Dissertation, Faculty of Mathematics and Physics, Charles University, Prague, 1976.
  3. D. Krupka, Geometric Problems of the Calculus of Variations on Fibered Spaces, Assoc. Prof. (Doc.) Dissertation, J. E. Purkyně University, Brno, 1980.
  4. D. Krupka, Natural Lagrangean structures, DrSc. Dissertation, Czechoslovak Academy of Sciences, Prague, 1981.

Edited proceedings

  1. Differential Geometry and Applications (Proc. Conf. Vol. 2, Nové Město na Moravě, Czechoslovakia, Sept. 1983 (D. Krupka, Ed.) J. E. Purkyně University, Brno, 1984).
  2. Differential Geometry and Its Applications (Proc. Conf., Brno, Czechoslovakia, August 1986 (D. Krupka and A. Švec, Eds.) Kluwer Academic Publishers, 1987).
  3. Differential Geometry and Its Applications (Proc. Conf., Brno, Czechoslovakia, August 1989 (J. Janyška and D. Krupka, Eds.) World Scientific, Singapore, 1990).
  4. Differential Geometry and Its Applications (Proc. 5th Internat. Conf., Opava, Czechoslovakia, August 1992 (O. Kowalski and D. Krupka, Eds.) Silesian University, Opava, 1993).
  5. Differential Geometry and Its Applications (Proc. 7th Internat. Conf., Brno, Czech Republic, August 1998, (I. Kolář, O. Kowalski, D. Krupka, and J. Slovák, Eds.) Masaryk Univ., Brno, 1999).
  6. Proceedings of the Seminar on Differential Geometry ((D. Krupka, Ed.) Silesian University at Opava, Opava, 2000).
  7. Differential Geometry and Its Applications (Proc. 8th International Conference on Diff. Geom. and Appl., Opava, Czech Republic, August 27-31, 2001, (O. Kowalski, D. Krupka, and J. Slovák, Eds.) Diff. Geom. Appl. 17 2002, special issue).
  8. Differential Geometry and Its Applications (Proc. Conf, August 2001, Opava, Czech Republic, (O. Kowalski, D. Krupka, and J. Slovák, Eds.) Silesian University in Opava, Opava, 2003).
  9. Global Analysis and Applied Mathematics (AIP Conference Proceedings 729, (K. Tas, D. Krupka, O. Krupková and D. Baleanu, Eds.) American Institute of Physics, 2004).
  10. Differential Geometry and Its Applications (Proc. Conf., Prague, August 2004 (J. Bureš, O. Kowalski, D. Krupka and J. Slovák, Eds.) Charles University in Prague, Czech Republic, 2005).
  11. Differential Geometry and its Applications (Proceedings of the 10th Int. Conf., Olomouc, August 2007 (O. Kowalski, D. Krupka, O. Krupková and J. Slovák, Eds.) World Scientific, Singapore, 2008).

Translations

  1. D. Krupka and I. Horová; V.M. Alexejev, V.M. Tichomirov and S.V. Fomin, Mathematical Theory of Optimal Processes (translation from Russian to Czech), Academia, Praha, 1991.

Unpublished notes, preprints

  1. D. Krupka, CP-noninvariant weak interactions of strongly interacting particles (in Slovak), Czechoslovak Students Scientific Activity 1965, Bratislava (Slovakia) (paper awarded the first prize in theoretical physics).
  2. D. Krupka, Differential Invariants (Lecture Notes) (Department of Algebra and Geometry, Faculty of Science, J.E. Purkyně University, Brno, 1979) 67 pp.
  3. D. Krupka, L. Klapka and J. Musilová, Geometric methods in the Calculus of Variations (Lecture Notes), Poprad 1984, J. E. Purkyně University, Brno, 1984 (in Czech).
  4. D. Krupka, The geometry of Lagrange Structures, Preprint Series in Global Analysis GA7/1997, Silesian University Opava, Czech Republic, 82 pp.
  5. D. Krupka, Elementary sheaf theory, Preprint Series in Global Analysis GA2/1998, Silesian University Opava, Czech Republic, 64 pp.
  6. D. Krupka, Smooth Manifolds, Preprint Series in Global Analysis GA14/2000, Silesian University Opava, Czech Republic, 31 pp.
  7. D. Krupka and M. Lenc, The Hilbert variational principle, Preprint 3/2002 GACR 201/00/0724, Masaryk University, Brno, 2002, 75 pp.
  8. A. Paták and D. Krupka, The Hilbert-Yang-Mills functional: Global theory, Preprint Series in Global Analysis, UP Olomouc, 2008.